My answer is slightly different from the one given in your textbook, because the area of the equilateral triangle should be square root(3)/ 4 * s squared

To solve these kind of rate of change problems, you can try to express the problem dA/ dt to the multiplication of two other derivates. Usually one of the derivative is given in the question (ds/ dt) and the other derivative can be found from a relationship or formula (dA/ ds is from the area of triangle formula)

Hope this helps!